OFF-RESONANT SELF-PHASE-MODULATION-INDUCED AND CROSS-PHASE-MODULATION-INDUCED MODULATION INSTABILITIES IN SINGLE-MODE RARE-EARTH-DOPED FIBER AMPLIFIERS

We present an analytical model of the self-and cross-phase-modulation- induced modulation instabilities in nonlinear, dispersive, homogeneous ly broadened, unsaturable fiber amplifiers. The rigorous treatment of the gain dispersion and of the gain-induced, near-resonance refractive -index dispersion permits description of the general case of arbitrary detuning between the laser frequency and the resonance and arbitrary bandwidth of the amplifying transition. Simple closed-form expressions are obtained for the combined gain coefficients and, in the self-phas e-modulation-induced case only, for the integrated gain. A qualitative ly new modulation-instability regime of an isolated wave in the normal group-velocity-dispersion region is described. (C) 1998 Optical Socie ty of America.